Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition bb being in the Serrin's regularity class, if the pressure pp belongs to Lα,γLα,γ with 2α+3γ⩽2 or the gradient field of pressure ∇p∇p belongs to Lα,γLα,γ with 2α+3γ⩽3 on [0,T][0,T], then the solution remains smooth on [0,T][0,T].